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Mathematics > Algebraic Geometry

Title: Some Properties of Internal Locale Morphisms Externalised

Abstract: We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective geometric morphisms and geometric embeddings, demonstrating that both can be computed `pointwise'. We also show that the co-frame operations on the co-frame of internal sublocales can also be computed `pointwise' too.
Comments: 46 pages. Updated version for submission. New sections on examples and applications, in addition to general improvements
Subjects: Algebraic Geometry (math.AG); Category Theory (math.CT)
MSC classes: 18B25 (Primary) 18F70 (Secondary)
Cite as: arXiv:2301.00961 [math.AG]
  (or arXiv:2301.00961v2 [math.AG] for this version)

Submission history

From: Joshua Wrigley [view email]
[v1] Tue, 3 Jan 2023 06:13:40 GMT (36kb)
[v2] Mon, 24 Jul 2023 16:15:23 GMT (43kb)

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